This paper establishes a unified a posteriori error estimator for a large class of conforming finite element methods for the Reissner-Mindlin plate problem. The analysis is based on some assumption (H) on the consistency of the reduction integration to avoid shear locking. The reliable and efficient a posteriori error estimator is robust in the sense that the reliability and efficiency constant...

The classical Euler–Bernoulli beam model and Kirchhoff plate are very useful on the macroscopic scale. In context of Eringen’s nonlocal elasticity theory, this article aims to develop criteria applicability nanoscale models based Timoshenko Mindlin via wave propagation theory. corresponding governing differential equations for derived by Hamilton’s principle, dispersion then obtained. By applyi...

the effect of a distributed patch mass on the natural frequency of vibration of a laminated rectangular plate with simply supported boundaries is investigated. the third order displacement field of a composite laminated rectangular plate is defined using the two variable refined plate theory. equations of motion of the plate are obtained with the help of calculus of variation. parametric study ...

Free vibration and buckling of three-phase bidirectional functionally graded sandwich (BFGSW) plates are studied in this paper for the first time by using an efficient nine-node quadrilateral (Q9) element. The core is pure ceramic, while two skin layers a material. element derived on basis Mindlin plate theory linked interpolations. Fundamental frequencies loads computed with various boundary c...

In a recent paper of Arnold et al. [D.N. Arnold, F. Brezzi, L.D. Marini, A family of discontinuous Galerkin finite elements for the Reissner–Mindlin plate, J. Sci. Comput. 22 (2005) 25–45], the ideas of discontinuous Galerkin methods were used to obtain and analyze two new families of locking free finite element methods for the approximation of the Reissner–Mindlin plate problem. By following t...

Abstract. In this paper, we derive and analyze a Reissner–Mindlin–like model for isotropic heterogeneous linearly elastic plates. The modeling procedure is based on a Hellinger– Reissner principle, which we modify to derive consistent models. Due to the material heterogeneity, the classical polynomial profiles for the plate shear stress are replaced by more sophisticated choices, that are asymp...

An ordinary state-based peridynamic (PD) model based on the Mindlin plate theory is presented to deal with fracture mechanics problems. Static and dynamic stress resultant intensity factors regarded as primary parameters for structures are evaluated by displacement extrapolation method. Owing PD surface effect, however, accuracy of field near crack surfaces significantly affected. Therefore, ar...

We consider the nite element (FE) approximation of the Reissner-Mindlin (RM) plate model, and indicate how to design meshes that yield accurate results when the p=hp version of the standard FE method is used. These guidelines allow quantities of engineering interest to be numerically predicted with great conndence near the boundary. We illustrate this through numerical computations in the case ...

A simple finite element method for the Reissner–Mindlin plate model in the primitive variables is presented and analyzed. The method uses nonconforming linear finite elements for the transverse displacement and conforming linear finite elements enriched by bubbles for the rotation, with the computation of the element stiffness matrix modified by the inclusion of a simple elementwise averaging. ...

Reliable and efficient residual-based a posteriori error estimates are established for the stabilised locking-free finite element methods for the Reissner-Mindlin plate model. The error is estimated by a computable error estimator from above and below up to multiplicative constants that do neither depend on the mesh-size nor on the plate’s thickness and are uniform for a wide range of stabilisa...